非高斯环境下基于最大相关熵的平滑估计器设计  

Smoothing estimator based on maximum correntropy in non-Gaussian environment

作　　者：马海平 刘婷 孙圣溢 费敏锐[2] MA Hai-ping;LIU Ting;SUN Sheng-yi;FEI Min-rui(Department of Electrical Engineering,Shaoxing University,Shaoxing Zhejiang 312000,China;School of Mechatronic Engineering and Automation,Shanghai University,Shanghai 200444,China)

机构地区：[1]绍兴文理学院电子工程系,浙江绍兴312000 [2]上海大学机电工程与自动化学院,上海200444

出　　处：《控制理论与应用》2024年第5期941-949,共9页Control Theory & Applications

基　　金：国家自然科学基金项目(61640316);浙江省自然科学基金项目(LY19F030011)资助。

摘　　要：针对Kalman平滑估计器在非高斯噪声环境下性能衰退问题,本文提出了一种基于最大相关熵准则作为最优估计标准的平滑估计方法,将其应用于固定滞后问题的状态估计,称之为固定滞后最大相关熵平滑估计器(FLMCS).首先,使用矩阵变换,给出最大相关熵Kalman滤波器的另一种形式;然后,以此为基础,通过引入新的状态变量来增广系统,并推导出所提平滑估计器的在线迭代方程;进一步比较平滑前后状态估计误差协方差,从理论上分析算法性能改进效果;最后,通过算例仿真验证所提平滑估计器在非高斯噪声干扰下的有效性和优越性.In order to overcome the performance degradation of Kalman smoothing estimator in non-Gaussian envi-ronment,this paper proposes a smoothing estimation method based on the maximum correntropy criterion as the optimal standard,for state estimation offixed-lag problem,which is calledfixed-lag maximum correntropy smoothing estimator(FLMCS).First,another form of maximum correntropy Kalmanfilter is given based on the matrix transform.Then,new state variables are introduced,and online iterative equations of the proposed FLMCS are derived through an augmented system.Furthermore,state estimation error covariances are compared before and after smoothing,and performance im-provement of the proposed FLMCS is analyzed theoretically.Finally,the illustrative examples are presented to verify the effectiveness and superiority of the proposed FLMCS in non-Gaussian noise environment.

关 键 词：平滑估计 KALMAN滤波 最大相关熵准则 固定滞后 非高斯环境 

分 类 号：TN713[电子电信—电路与系统]